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MHT CET · Physics · Magnetic Effects of Current

A circular arc of radius r carrying current ' \(I\) ' subtends an angle \(\frac{\pi}{8}\) at its entre. The radius of a metal wire is uniform. The magnetic induction at the centre of circular arc is ( \(\mu_0=\) permeability of free space)

  1. A \(\frac{\mu_0 \mathrm{I}}{8 \mathrm{r}}\)
  2. B \(\frac{\mu_0 I}{32 r}\)
  3. C \(\frac{\mu_0 \mathrm{I}}{64 \mathrm{r}}\)
  4. D \(\frac{\mu_0 \mathrm{I}}{16 \mathrm{r}}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{\mu_0 I}{32 r}\)

Step-by-step Solution

Detailed explanation

The magnetic induction at the centre of circular arc is
\(B=\frac{\mu_0 I}{4 \pi r} \times \theta\)
\(\therefore \quad B=\frac{\mu_0 \dot{I}}{4 \pi r} \times \frac{\pi}{8} \quad \cdots\left[\because \theta=\frac{\pi}{8}\right]\)
\(\therefore \quad B=\frac{\mu_0 I}{32 r}\)